"I think we're fairly close, but we have to get massive security ... Mitch [McConnell] is on board, Paul Ryan's on board," Trump said before he left for hurricane-ravaged Florida.

Schumer and Pelosi followed up Thursday by saying, "What remains to be negotiated are the details of border security, with a mutual goal of finalizing all details as soon as possible."

Ryan on Thursday said he supports passing DACA protections attached to other border security measures. But he and other Republican leaders indicated that a deal could be further away than the Democrats hope.

"There is no agreement. The president and the chief of staff called me from Air Force One today to discuss what was discussed. And it was a discussion, not an agreement or a negotiation," said Ryan, who did not attend the dinner.

"You cannot fix DACA without fixing the root cause of the problem," the Wisconsin Republican added. "We do not have control of our borders. So, we need border security and enforcement as part of any agreement. I think that's something the Democrats are beginning to understand."

Senate Majority Leader Mitch McConnell on Thursday appeared to believe an agreement is not imminent.

"As Congress debates the best ways to address illegal immigration through strong border security and interior enforcement, DACA should be part of those discussions. We look forward to receiving the Trump administration's legislative proposal as we continue our work on these issues," he said.

McConnell's No. 2 in the Senate, Majority Whip John Cornyn, on Thursday said, "it looks like a deal to make a deal." The other members of Congress "will have some ideas about what that will look like and what will actually pass," he added.

Still, some of Trump's most loyal supporters in the right-wing media decried Trump's efforts to strike a deal with Democrats. The website Breitbart News, which staunchly supported Trump as a candidate, labeled him "Amnesty Don" and said he caved on DACA.